C₄₃×#64470 #27166378

order	12900
isoclinism	isoclinic class of #3874
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₄₃×#64470

Splittings

derived, Hall	C₅²⋊C₃ ⋊ C₄×C₄₃
Hall	C₄₃×C₅²⋊C₃ ⋊ C₄
Hall	C₅²×C₄₃ ⋊ Dic₃
Sylow	C₅² ⋊ Dic₃×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₃	#3874
commutator, hypocenter	C₅²⋊C₃	C₄×C₄₃
Frattini	C₂	C₄₃×#3874
Fitting, socle	C₂×C₅²×C₄₃	D₃
prime radical	C₂×C₄₃×C₅²⋊C₃	C₂
cosocle	C₂×C₅²⋊C₃	C₂×C₄₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂×C₄₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 2580

A minimal faithful permutation representation — 2 generators on 62 points:

(1,7)(2,4,6,13,5,9,12,10,11,14)(3,15)(16,19,18,17)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(1,2,4)(3,6,14)(5,10,8)(7,11,13)(9,15,12)

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 47);

C43×#64470 #27166378